Course title
V0640400
Linear Space

 shimizu kenichi Click to show questionnaire result at 2018
Course description
This course introduces basic notions in linear algebra in a more abstract form. The theory of linear space is an essential knowledge for studying advanced topics, such as functional analysis, control theory, quantum mechanics, etc.
Purpose of class
To understand the basics on linear spaces and learn basics for more advanced courses, such as functional analysis, control theory, quantum mechanics, etc.
Goals and objectives
  1. Understand the notion of linear independence
  2. Understand the notions of linear spaces and linear maps
  3. Understand the notion of Jordan canonical form and how to compute it
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Linear space Review Linear Algebra I and II 180minutes
2. Linear maps Review the notion of linear spaces 180minutes
3. Basis and dimension Review the notions of the rank and the determinant of a matrix (from Linear Algebra I and II) 180minutes
4. Matrix representation of a linear map Review the notion of a basis of a linear space 180minutes
5. The image and the kernel of a linear map (1) Definition and their basic properties Review the notion of a basis of a linear subspace 180minutes
6. The image and the kernel of a linear map (1) How to compute them Review the method to solve a system of linear equations (Gaussian Elimination) 180minutes
7. Mid-term exam Review the content of this course 270minutes
8. Change-of-basis matrix Review the notion of the representing matrix 180minutes
9. Matrix diagonalization Review the diagonzalization of matrices (from Linear Algebra I and II) 180minutes
10. Generalized eigenspaces Review the notions of eigenvalues and eigenvectors 180minutes
11. Jordan canonical form (1) Existence Review the last class 180minutes
12. Jordan canonical form (1) Computation Review the last class 180minutes
13. Jordan canonical form (1) Applications Review the last class 180minutes
14. Final exam Review the content of this course 270minutes
Total. - - 2700minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Report Total.
1. 10% 10% 10% 30%
2. 10% 10% 10% 30%
3. 10% 10% 20% 40%
Total. 30% 30% 40% -
Evaluation method and criteria
Evaluate by the scores of the mid-term exam, the final exam and other reports.
Textbooks and reference materials
参考書：齋藤正彦 著『齋藤正彦 線型代数学』（東京出版）
Prerequisites
Linear Algebra I and II are assumed.
Office hours and How to contact professors for questions
  • 12:30-13:10 of Monday, or anytime I'm in the lab.
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
N/A
Last modified : Wed Oct 17 07:48:54 JST 2018